Prop bet

DrPublo · #1 07-07-2005, 12:57 PM

X-posted from the other gambling forum.

I'm playing 1/2 NL last night and the following prop bet comes up. Player A asks me to pick a hand to play heads up, AK or 22. I tell him 22. He suggests prop betting it as follows:

Each hand, he has an "imaginary" Ac Kc, and each hand I have an imaginary red 33 (after I lost the first two bets I switched to 33 from 22). I mean imaginary in the sense that it is as if we are dealing with a 56 card deck, with 2 Ac, 2 Kc, 2 3d and 2 3h. Every time a hand gets to a river, we compare our imaginary hands with the board, and the loser pays the winner $5. Duplicate cards are allowed, so he can make a pair of aces with 2 Acs, or a AAKKx flush, and I can make 6 treys, etc.

The question is who is a favorite in this bet. I think I am. If we were dealing with just a regular deck, 33 is basically a coinflip vs AK. But in our imaginary setup I have twice as many cards to hit a set, which gives me a huge advantage. Of course, he has 8 pair outs instead of 6, and when he flops a flush draw he has 11 outs to make it, instead of 9. So take some away from me there.

I also think there might be a bias based on the stipulation that the hand must see a river. I suspect that boards with As and Ks on them are more likely to see a river than boards with all low cards. I wonder how this affects the bet as well.

Anyway, if someone could help me run the numbers on this prop bet I'd be very interested.

The Doc

MikeL05 · #2 07-07-2005, 01:10 PM

Actually, hitting a set in this matchup is sort of a secondary way to win. Most of these runs that you win will be due to him not pairing at all, as opposed to him pairing and you hitting your set to beat that.

Remember that, preflop, it is him who is drawing. And he had a 46% chance of winning with 6 remaining K/A cards. Now he has 8. I actually think you're behind in this bet.

LetYouDown · #3 07-07-2005, 01:17 PM

Odds that an A or K will appear:

1 - 44 C 5/52 C 5 = 58.2%

Odds that a 2 will appear:

1 - 48 C 5/52 C 5 = 34.1%

meow_meow · #4 07-07-2005, 01:42 PM

So the odds that an A and/or a K will hit the board, but not a 3 (which is obviously the most common way for AKs to win) go from 43.7% normally down to 38.4% - looking good on that front.

Of the other ways AK can win, straights and double paired boards look to be a push (I think), and he probably gets a slight advantage from the extra flush outs.

It seems likely to me that if every hand went to showdown, you would be ahead. The showdown factor is obviously key though, and may be a much larger effect than the extra 3's in the deck.

DrPublo · #5 07-07-2005, 04:15 PM

[ QUOTE ]
Odds that an A or K will appear:

1 - 44 C 5/52 C 5 = 58.2%

Odds that a 2 will appear:

1 - 48 C 5/52 C 5 = 34.1%

[/ QUOTE ]

What are the odds that a) an A and a 3 appear, b) a K and a 3 appear, and c) an A, K and 3 appear.

The Doc